Module FOUN0257: MATHS APPLICATIONS 1

Department: Foundation Year [Queen's Campus, Stockton]

FOUN0257: MATHS APPLICATIONS 1

Pre-requisites

Corequisites

Excluded Combinations

Aims

• To extend and develop knowledge of the six trigonometrical functions and inverses.
• to introduce and develop a knowledge of matrices and their applications.
• to introduce and develop a knowledge of first and second order differential equations and their applications
• to extend knowledge of Cartesian coordinates in two and three dimensions to include equations of circles, lines and planes.
• to introduce the concept of polar coordinates.
• to extend and develop knowledge of complex numbers.
• to develop a knowledge of vectors and their applications in two and three dimensions to include equations of lines and planes

Content

• trigonometrical functions of angles, real numbers and graphs.
• Cartesian equations in two and three dimensions of straight lines, perpendicular lines and circles.
• complex numbers: +, -, x, /, complex conjugate, polar form, Argand diagrams, De Moivre's theorem.
• vectors in two and three dimensions including: use of column and unit vectors, addition, subtraction and multiplication by scalar.
• Scalar (dot) and vector (cross) product and their applications.
• vector equations of lines and planes.
• Matrices 2x2 and nxm, addition, subtraction and multiplication, determinant, transpose and inverse. Applications to simultaneous equations.
• First Order Differential equations including separating variables.
• Second Order Differential equations.

Learning Outcomes

• By the end of the module the student will have acquired the skills to be able to:
• select and use trigonometric and techniques as required in problems appropriate to the syllabus.
• confidently manipulate a range of Cartesian and vector equations in two and three dimensions.
• plot a graph using polar coordinates.
• understand and use complex numbers in a range of situations as appropriate to the syllabus.
• use matrices in a number of mathematical situations.
• understand and use first and second order differential equations in a range of situations as appropriate to the syllabus.

• By the end of the module the student will:
• be able to communicate effectively in writing
• be able to apply number in the tackling of numerical problems
• be able to demonstrate problem solving skills

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Theory, initial concepts and techniques will be introduced during lectures.
• Much of the learning, understanding and consolidation will take place through the use of structured worksheets during tutorials and students' own time.
• Ability to recall, select and use knowledge will be tested by: a coursework portfolio containing students solutions to questions or tasks set by the tutor on a weekly basis, mid-module invigilated test and an end of module invigilated test.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment

Weekly self-testing units